<?xml version="1.0" encoding="us-ascii"?><InstanceReport xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xsd="http://www.w3.org/2001/XMLSchema"><Version>2.2.0.25</Version><hasSegments>true</hasSegments><hasScenarios>false</hasScenarios><ReportLongName>0100004 - Document - Risk Return Summary - Artio Local Emerging Markets Debt Fund {Unlabeled}</ReportLongName><DisplayLabelColumn>false</DisplayLabelColumn><ShowElementNames>false</ShowElementNames><RoundingOption /><HasEmbeddedReports>false</HasEmbeddedReports><Columns><Column><Id>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelColumn>false</LabelColumn><CurrencyCode /><FootnoteIndexer /><hasSegments>true</hasSegments><hasScenarios>false</hasScenarios><MCU><KeyName>{dei_DocumentInformationDocumentAxis} : Artio Local Emerging Markets Debt Fund
3/2/2010 - 3/1/2011
</KeyName><CurrencySymbol /><contextRef><ContextID>TwelveMonthsEnded_01Mar2011_S000030284_Member</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0000887210</EntityValue><PeriodDisplayName /><PeriodType>duration</PeriodType><PeriodStartDate>2010-03-02T00:00:00</PeriodStartDate><PeriodEndDate>2011-03-01T00:00:00</PeriodEndDate><Segments><anyType xsi:type="Segment"><IsDefaultForEntity>false</IsDefaultForEntity><Name /><IsFromEntityGroup>false</IsFromEntityGroup><ValueName>Artio Local Emerging Markets Debt Fund</ValueName><ValueType>dei_DocumentInformationDocumentAxis</ValueType><Namespace>xbrldi</Namespace><Schema>http://xbrl.org/2006/xbrldi</Schema><DimensionInfo><Id>agif887210_S000030284Member</Id><dimensionId>dei_DocumentInformationDocumentAxis</dimensionId><type>explicitMember</type></DimensionInfo></anyType></Segments><Scenarios /></contextRef><UPS /><CurrencyCode /><OriginalCurrencyCode /></MCU><CurrencySymbol /><Labels /></Column></Columns><Rows><Row><Id>3</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><Level>0</Level><ElementName>agif887210_SupplementTextBlock</ElementName><ElementPrefix>agif887210</ElementPrefix><IsBaseElement>false</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><ShortDefinition>Supplement</ShortDefinition><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsSubReportEnd>false</IsSubReportEnd><IsCalendarTitle>false</IsCalendarTitle><IsTuple>false</IsTuple><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole>verboselabel</PreferredLabelRole><FootnoteIndexer /><Cells><Cell><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText>&lt;p&gt;&lt;b&gt;&lt;u&gt;ARTIO GLOBAL FUNDS&lt;/u&gt;&lt;/b&gt;&lt;/p&gt;&lt;p&gt;&lt;b&gt; Artio Local Emerging Markets Debt Fund&lt;/b&gt;&lt;/p&gt;&lt;p&gt;&lt;b&gt; Supplement dated April 22, 2011 to the&lt;/b&gt;&lt;/p&gt;&lt;p&gt;&lt;b&gt; Prospectus dated March 1, 2011&lt;/b&gt;&lt;/p&gt;&lt;p&gt;&lt;b&gt;This supplement provides new and additional information beyond that contained in the Prospectus and should be retained and read in conjunction with the Prospectus.&lt;/b&gt;&lt;/p&gt;</NonNumbericText><NonNumericTextHeader /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios></Cell></Cells><OriginalInstanceReportColumns /><Unit>Other</Unit><ElementDataType>us-types:textBlockItemType</ElementDataType><SimpleDataType>string</SimpleDataType><ElementDefenition>Supplement</ElementDefenition><ElementReferences>No authoritative reference available.</ElementReferences><IsTotalLabel>false</IsTotalLabel><IsEPS>false</IsEPS><Label>Supplement [Text Block]</Label></Row><Row><Id>4</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><Level>0</Level><ElementName>agif887210_SupplementPrincipalInvestmentStrategiesTextBlock</ElementName><ElementPrefix>agif887210</ElementPrefix><IsBaseElement>false</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><ShortDefinition>Supplement Principal Investment Strategies.</ShortDefinition><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsSubReportEnd>false</IsSubReportEnd><IsCalendarTitle>false</IsCalendarTitle><IsTuple>false</IsTuple><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole>verboselabel</PreferredLabelRole><FootnoteIndexer /><Cells><Cell><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText>&lt;p&gt;&lt;i&gt;&lt;b&gt;In the section entitled &amp;#8220;Principal Investment Strategies&amp;#8221; beginning on page 49, the first bulleted item is replaced with the following:&lt;/b&gt;&lt;/i&gt;&lt;/p&gt;&lt;p&gt; Under normal circumstances, the Fund will invest at least 80% of its net assets (including fixed income related futures, options, swaps and other instruments as well as borrowings for investment purposes) in fixed income and short term money market instruments including forward foreign exchange contracts denominated in emerging market currencies. The Fund may invest in derivatives denominated in any currency and such instruments will be included under the 80% of net assets policy provided the underlying asset is a fixed income or currency instrument denominated in an emerging market currency. In defining emerging markets, the Adviser may consider, but is not bound by the classifications of the World Bank and will generally invest in countries other than the U.S., Japan, Australia, Canada, New Zealand and the developed countries in Western Europe. The Fund will provide shareholders with at least 60 days notice prior to any changes in this policy&lt;/p&gt;</NonNumbericText><NonNumericTextHeader /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios></Cell></Cells><OriginalInstanceReportColumns /><Unit>Other</Unit><ElementDataType>us-types:textBlockItemType</ElementDataType><SimpleDataType>string</SimpleDataType><ElementDefenition>Supplement Principal Investment Strategies.</ElementDefenition><ElementReferences>No authoritative reference available.</ElementReferences><IsTotalLabel>false</IsTotalLabel><IsEPS>false</IsEPS><Label>Supplement Principal Investment Strategies Text Block</Label></Row></Rows><Footnotes /><NumberOfCols>1</NumberOfCols><NumberOfRows>2</NumberOfRows><ReportName>Risk Return Summary - Artio Local Emerging Markets Debt Fund (Artio Local Emerging Markets Debt Fund)</ReportName><MonetaryRoundingLevel>UnKnown</MonetaryRoundingLevel><SharesRoundingLevel>UnKnown</SharesRoundingLevel><PerShareRoundingLevel>UnKnown</PerShareRoundingLevel><ExchangeRateRoundingLevel>UnKnown</ExchangeRateRoundingLevel><HasCustomUnits>false</HasCustomUnits><SharesShouldBeRounded>true</SharesShouldBeRounded></InstanceReport>
